Graph Neural Networks (GNNs) have been a powerful tool to acquire high-quality node representations dealing with graphs, which strongly depends on a promising graph structure. In the real world scenarios, it is inevitable to introduce noises in graph topology. To prevent GNNs from the disturbance of irrelevant edges or missing edges, graph structure learning is proposed and has attracted considerable attentions in recent years. In this paper, we argue that current graph structure learning methods still pay no regard to the status of nodes and just judge all of their connections simultaneously using a monotonous standard, which will lead to indeterminacy and instability in the optimization process. We designate these methods as status-unaware models. To demonstrate the rationality of our point of view, we conduct exploratory experiments on publicly available datasets, and discover some exciting observations. Afterwards, we propose a new model named Graph Structure Learning via Progressive Strategy (PROSE) according to the observations, which uses a progressive strategy to acquire ideal graph structure in a status-aware way. Concretely, PROSE consists of progressive structure splitting module (PSS) and progressive structure refining module (PSR) to modify node connections according to their global potency, and we also introduce horizontal position encoding and vertical position encoding in order to capture fruitful graph topology information ignored by previous methods. On several widely-used graph datasets, we conduct extensive experiments to demonstrate the effectiveness of our model, and the source code 1 https://github.com/tigerbunny2023/PROSE is provided.

While Graph Neural Networks (GNNs) have become de facto criterion in graph representation learning, they still suffer from label scarcity and poor generalization. To alleviate these issues, graph pre-training has been proposed to learn universal patterns from unlabeled data via applying self-supervised tasks. Most existing graph pre-training methods only use a single self-supervised task, which will lead to insufficient knowledge mining. Recently, there are also some works that try to use multiple self-supervised tasks, however, we argue that these methods still suffer from a serious problem, which we call it graph structure impairment. That is, there actually exists structural gaps among several tasks due to the divergence of optimization objectives, which means customized graph structures should be provided for different self-supervised tasks. Graph structure impairment not only significantly hurts the generalizability of pre-trained GNNs, but also leads to suboptimal solution, and there is no study so far to address it well. Motivated by Meta-Cognitive theory, we propose a novel model named Core Graph Cognizing and Differentiating (CORE) to deal with the problem in an effective approach. Specifically, CORE consists of cognizing network and differentiating process, the former cognizes a core graph which stands for the essential structure of the graph, and the latter allows it to differentiate into several task-specific graphs for different tasks. Besides, this is also the first study to combine graph pre-training with cognitive theory to build a cognition-aware model. Several experiments have been conducted to demonstrate the effectiveness of CORE.

Based on the celebrated public goods game with group interaction, we study the evolution of cooperation on two kinds of scale-free networks with similar degree distribution and clustering coefficient. It is showed that there are different evolution routes in the structured population. The metric clusters existing on the popularity-similarity network let cooperation diffuse in local regions. Whereas, cooperators on the clustered scale-free network tend to invade hubs firstly, and then spread from hubs to leaves with a top-down pattern, which leads to the higher cooperation level on the clustered scale-free network than that on the popularity-similarity network.